KyFanNorm

KyFanNorm
Computes the Ky Fan k-norm of an operator
Other toolboxes required	none
Related functions	kpNorm SchattenNorm TraceNorm

KyFanNorm is a function that computes the Ky Fan k-norm of an operator (i.e., the sum of its k largest singular values). It works with both full and sparse matrices.

Syntax

• NRM = KyFanNorm(X,K)

Argument descriptions

• X: An operator to have its Ky Fan K-norm computed.
• K: A positive integer.

Examples

Equals the operator norm when K = 1 (but faster!)

The Ky Fan 1-norm is just the operator norm, which is implemented in MATLAB by the norm function. However, the KyFanNorm function is typically faster than the norm function:

>> X = rand(2500);
>> tic; KyFanNorm(X,1)
   toc

ans =

       1250.2

Elapsed time is 0.861377 seconds.
>> tic; norm(X)
   toc

ans =

       1250.2

Elapsed time is 4.288788 seconds.